A real op amp draws current through its inputs which has to be over a minimum limit for the op amp to work properly. If the external resistors are very high then the voltages internally will not be able to adjusted in such a way that the input current is what required.

While input current in some op amps can be a problem if large resistor values are used, CMOS op amps draw so little input current that 1MΩ will not be a problem. However, parasitic capacitance combined with high resistance values can result in nonideal behavior.
Also, resistors generate voltage noise proportional to the square root of the resistance, all other factors being equal. In high gain, wide bandwidth circuits, high resistor values can result in excessive noise.